Efficient Reasoning for Inconsistent Horn Formulae

  • Joao Marques-SilvaEmail author
  • Alexey Ignatiev
  • Carlos Mencía
  • Rafael Peñaloza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10021)


Horn formulae are widely used in different settings that include logic programming, answer set programming, description logics, deductive databases, and system verification, among many others. One concrete example is concept subsumption in lightweight description logics, which can be reduced to inference in propositional Horn formulae. Some problems require one to reason with inconsistent Horn formulae. This is the case when providing minimal explanations of inconsistency. This paper proposes efficient algorithms for a number of decision, function and enumeration problems related with inconsistent Horn formulae. Concretely, the paper develops efficient algorithms for finding and enumerating minimal unsatisfiable subsets (MUSes), minimal correction subsets (MCSes), but also for computing the lean kernel. The paper also shows the practical importance of some of the proposed algorithms.


Description Logic Lean Kernel Deductive Database Horn Formula Definite Clause 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Joao Marques-Silva
    • 1
    Email author
  • Alexey Ignatiev
    • 1
    • 4
  • Carlos Mencía
    • 2
  • Rafael Peñaloza
    • 3
  1. 1.University of LisbonLisbonPortugal
  2. 2.University of OviedoOviedoSpain
  3. 3.Free University of Bozen-BolzanoBolzanoItaly
  4. 4.ISDCT SB RASIrkutskRussia

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